Transcript Lecture 6

Evolutionary Computational
Inteliigence
Lecture 6a:
Multimodality
Multimodality
Most interesting problems have more than one
locally optimal solution and our goal is to
detect all of them
Multi-Objective Problems (MOPs)
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Wide range of problems can be categorised
by the presence of a number of n possibly
conflicting objectives:
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buying a car: speed vs. price vs. reliability
Two part problem:
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finding set of good solutions
choice of best for particular application
MOP Car example
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I want to buy a car
I would like it’s the cheapest the possible (minimize f1)
and the most comfortable the possible (maximize f2)
If I consider the two functions separately I obtain:
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min f1
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max f2
MOPs 1: Conventional approaches
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rely on using a weighting of objective
function values to give a single scalar
objective function whichn can then be
optimised:
f ' ( x)   wi f i ( x)
i 1
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to find other solutions have to re-optimise
with different wi.
MOPs 2: Dominance
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we say x dominates y if it is at least as good
on all criteria and better on at least one
f2
Pareto front
x
Dominated by x
f1
Implications for Evolutionary
Optimisation
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Two main approaches to diversity maintenance:
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Implicit approaches (decision space):
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Impose an equivalent of geographical separation
Impose an equivalent of speciation
Explicit approaches (fitness):
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Make similar individuals compete for resources
(fitness)
Make similar individuals compete with each other
for survival
Implicit 1: “Island” Model Parallel
EAs
EA
EA
EA
EA
EA
Periodic migration of individual solutions between populations
Island Model EAs:
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Run multiple populations in parallel, in some
kind of communication structure (usually a
ring or a torus).
After a (usually fixed) number of generations
(an Epoch), exchange individuals with
neighbours
Repeat until ending criteria met
Partially inspired by parallel/clustered
systems
Island Model Parameter Setting
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The idea is simple but its success is subject to a
proper parameter setting
It must be somehow known the number of
“islands”,i.e. basins of attraction we are considering
It must be set the population size for each separate
island
If some a priori information regarding the fitness
landscape is given, island model can be efficient,
otherwise it can likely fail
Implicit 2: Diffusion Model Parallel
EAs
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Impose spatial structure (usually grid) in 1
pop
Current
individual
Neighbours
Diffusion Model EAs
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Consider each individual to exist on a point
on a grid
Selection (hence recombination) and
replacement happen using concept of a
neighbourhood a.k.a. deme
Leads to different parts of grid searching
different parts of space, good solutions
diffuse across grid over a number of gens
Diffusion Model Example
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Assume rectangular grid so each individual has 8
immediate neighbours
For each point we can consider a population mad up
of 9 individuals
One of the other 8 remaining point is selected (e.g.
by means of roulette wheel)
Recombination between starting and selected point
occurs
In a steady state logic replacement of the fittest
occurs
Implicit 3: Automatic Speciation
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It restricts the recombination on the basis genotypic
structure of the solutions in order to have recombination
only amongst individual of the same specie
– comparing the maximum genotypic distance between
solutions
– Adding a “tag” (genotypic enlargement) in order to
characterize the belonging of each individual to a
certain specie
In both cases, problem requires a lot of comparisons
and the computational overhead can be very high
Explicit 1: Fitness Sharing
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Restricts the number of individuals within a given
niche by “sharing” their fitness, so as to allocate
individuals to niches in proportion to the niche fitness
need to set the size of the niche share in either
genotype or phenotype space
run EA as normal but after each gen set
f ' (i ) 
f (i )
1  d /  d  
sh (d )  
 sh(d (i, j ))
 0 otherwise

j 1
Meaning of the distance is
representation dependent
Explicit 2: Crowding
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Attempts to distribute individuals evenly
amongst niches
relies on the assumption that offspring will tend
to be close to parents
randomly selects a couple of parents, produce
2 offspring
each offspring compete in a pairtournament for surviving with the most
similar parent (steady state) i.e. the parent
which has minimal distance
Fitness Sharing vs. Crowding
Fitness Sharing
Crowding
Multimodality and Constraints
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In some cases we are not satisfied by finding
all the local optima but only a subset of them
having certain properties (e.g. fitness values)
In such cases the combination of algorithmic
components can be beneficial
A rather efficient and simple option is to
properly combine a cascade
Fast Evolutionary Deterministic
Algorithm (2006)
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FEDA is composed by:
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Quasi Genetic Algorithm (QGA, 2004)
Fitness Sharing Selection Scheme (FSS)
Multistart Hooke Jeeves Algorithm (HJA)
Quasi Genetic Algorithm
FEDA
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The set of solutions coming from QGA
(usually a lot) are processed by FSS
We thus obtain a smaller set of points which
have good fitness values and are spread out
in the decision space
The HJA is then applied to each of those
solutions
Grounding Grid Problem 1
Grounding Grid Problem 2
Grounding System Problem
Evolutionary Computational
Inteliigence
Lecture 6b: Towards
Parameter Control
Motivation 1
An EA has many strategy parameters, e.g.
 mutation operator and mutation rate
 crossover operator and crossover rate
 selection mechanism and selective pressure (e.g.
tournament size)
 population size
Good parameter values facilitate good performance
Q1 How to find good parameter values ?
Motivation 2
EA parameters are rigid (constant during a run)
BUT
an EA is a dynamic, adaptive process
THUS
optimal parameter values may vary during a
run
Q2: How to vary parameter values?
Parameter tuning
Parameter tuning: the traditional way of testing and
comparing different values before the “real” run
Problems:
 users mistakes in settings can be sources of errors
or sub-optimal performance
 costs much time
 parameters interact: exhaustive search is not
practicable
 good values may become bad during the run
(e.g. Population size)
Parameter Setting: Problems
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A wrong parameter setting can lead to an
undesirable algorithmic behavious since it can lead
to stagnation or premature convergence
Too large population size, stagnation
Too small population size, premature convergence
In some “moments” of the evolution I would like to
have a large pop size (when I need to explore and
prevent premature convergence); in other
“moments” I would like to have a small one
(when I need to exploit available genotypes)
Parameter control
Parameter control: setting values on-line, during the
actual run, I would like that the algorithm “decides” by
itself how to properly vary parameter setting over the
run
Some popular options for pursuing this aim are:
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predetermined time-varying schedule p = p(t)
using feedback from the search process
encoding parameters in chromosomes and rely on natural
selection (similar to ES self-adaptation)
Related Problems
Problems:
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finding optimal p is hard, finding optimal p(t) is harder
still user-defined feedback mechanism, how to ”optimize”?
when would natural selection work for strategy parameters?
Provisional answer:
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In agreement with the No Free Lunch Theorem, optimal control
strategy does not exist. Nevertheless, there are a plenty of
interesting proposals that can be very performing in some problems.
Some of these strategies are very problem oriented while some others
are much more robust and thus applicable in a fairly wide spectrum of
optimization problems